Abstract
We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, \(RCD^*(K,N),\) is a Lie group. We obtain an optimal upper bound on the dimension of this group, and classify the spaces where this maximal dimension is attained.
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L. Guijarro and J. Santos-Rodríguez were supported by research Grants MTM2014-57769-3-P (MINECO) and ICMAT Severo Ochoa Project SEV-2015-0554 (MINECO). J. Santos-Rodríguez was supported by a Ph.D. Scholarship awarded by Conacyt.
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Guijarro, L., Santos-Rodríguez, J. On the isometry group of \(RCD^*(K,N)\)-spaces. manuscripta math. 158, 441–461 (2019). https://doi.org/10.1007/s00229-018-1010-7
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DOI: https://doi.org/10.1007/s00229-018-1010-7